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Left-hand Side And Right-hand Side Of An Equation




More generally, these terms may apply to an Inequation or Inequality . In the ''inequality case'', there is no symmetry. The right-hand side is everything on the right side of a Test Operator in an Expression . Conversely, the '''left-hand side''' is everything on the left side.


SOME EXAMPLES


In

:2''a'' + 5 = ''a''/3,

the Term

a


is the RHS.

In

x


just

:10

is the RHS.


HOMOGENEOUS AND INHOMOGENEOUS EQUATIONS


In solving mathematical equations, particularly Linear Simultaneous Equations , Differential Equation s and Integral Equation s, the terminology ''homogeneous'' is often used for equations with the RHS set equal to zero. The corresponding ''inhomogeneous'' or ''nonhomogeneous'' equation then has the RHS with some given data, but of a general character.

The typical case is of some Operator ''L'', with the difference being that between the equation

Lf


to be solved for a function ''f'', and the equation

Lf


with ''g'' a fixed function, to solve again for ''f''. The point of the terminology appears for ''L'' a Linear Operator . Then any solution of the inhomogeneous equation may have a solution of the homogeneous equation added to it, and still remain a solution.

For example in Mathematical Physics , the homogeneous equation may correspond to a physical theory formulated in Empty Space , while the inhomogeneous equation asks for more 'realistic' solutions with some matter, or charged particles.


SYNTAX


More abstractly, when using Infix notation

  • ''U''


  • . This usage is less common, though.



SEE ALSO